The integral is : $\displaystyle \lim_{n\rightarrow \infty} \int_{\mathbb{R}^2}e^{-(x^2+y^2)^n}dxdy$
How could I solve this integral?
I've tried polar coordinates, but then I get $\displaystyle \lim_{n\rightarrow \infty} \int_{0}^{\infty}e^{-r^{2n}}r2\pi \,dr$, and I don't know how to solve this...
Any help would be appreciated.